Derivative and Power Rule

Q:  Find f ‘ (t) if f(t) = sqrt(3)/t^4

(using the power rule)

Answer:

Step 1)  Rewrite the problem to get t^4 out of the denominator:

sqrt(3)/t^4 = sqrt(3)*t^-4

So, now take the derivative of sqrt(3)*t^-4

Remember, “sqrt(3)” is a constant multiplier, so it just stays along for the ride.  The power rule tells you to bring the exponent down as a multiplier and then subtract 1 from the exponent, like so:

f(t) = sqrt(3)*t^-4

f ‘ (t) = sqrt(3)*(-4)*t^(-4-1)

f ‘ (t) = -4*sqrt(3)t^-5  [final answer]

You could rewrite f ‘ (t) to putt back in the denominator like so:

f ‘ (t) = -4*sqrt(3) / t^5

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